Question

If wavelength of the first line of the Paschen series of hydrogen atom is _____ nm, then the wavelength of the second line of this series is nm. (Nearest integer)

Answer 1

Answer: 492

$\frac{1}{{\left({\lambda }_1\right)}_P}=R_H{Z}^2\left(\frac{1}{9}-\frac{1}{16}\right)$
$\frac{1}{{\left({\lambda }_2\right)}_P}=R_H{Z}^2\left(\frac{1}{9}-\frac{1}{25}\right)$
$\frac{{\left({\lambda }_2\right)}_P}{{\left({\lambda }_1\right)}_P}=\frac{\frac{7}{16\times 9}}{\frac{16}{25\times 9}}=\frac{25\times 7}{16\times 16}$
${\left({\lambda }_2\right)}_P=\frac{25\times 7}{16\times 16}\times 720$
${\left({\lambda }_2\right)}_P=492nm$